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The photoelectric troll (all that and a bag of chips!)

April 3, 2013 by Matthew Rave

Somewhere in the wilderness of Toelek is a store.  Inside the store are clerks.  The clerks sell bags of Wavy Lay’s potato chips:

Wavy Lays Original

Now, the thing is, if you give money to clerks to buy some chips, the clerks never give any money back: they’re greedy.  What’s more, they leave the store immediately with whatever money they have left over from the transaction.  However, the clerks don’t always get very far, because out behind the store is a bridge that the clerks have to cross, and the bridge is guarded by a troll named Voltar.  The troll is greedy, too.  He demands a toll, and if a clerk can’t pay up then he can’t cross the bridge.

Toelek is a weird place.  Its citizens have a very rigid society, and people are required to wear differently colored clothing depending upon how much money they have in their pocket.  The money is always in multiple of 50 cents.  For example, if you carry $0.50 then you must wear red; if you carry $1.00 you must wear orange; if you carry $1.50 you must wear yellow.

Look, over there—I see a line of people approaching the store.  They’re all wearing red.  They enter the store…but I don’t see any clerks exiting out the back, and consequently no clerks cross the bridge.  More and more reds go into the store, and a faster and faster rate, but it doesn’t matter.  There are no clerks coming out.  The troll doesn’t get any business.

I conclude that a bag of chips costs more than $0.50.

Later, I see a line of oranges go into the store.  I now observe some clerks coming out, but none of these can cross the bridge.  I conclude that chips cost $1.00, but since the clerks have no money left over, they can’t pay the troll’s toll.

Even later, I see a line of yellows go into the store.  Clerks are coming out, and these can cross the bridge.  The troll must be demanding a toll of $0.50 or less.

There are many quantities which are important in analyzing this situation: the amount of money a person has before entering the store (use E for entering), the price of a bag of Wavy Lay’s potato chips (let’s call this price W), the toll that Voltar the troll demands (let’s call this V), and the amount of money a clerk has, K (they speak Dutch in Toelek, so the clerks are called klerks) upon exiting the store.  It should be obvious that

K = E – W,

since the amount of money a clerk has upon leaving the store is just the amount of money a person has upon entering the store minus the cost of some chips.  Additionally, for a clerk to cross the bridge, it must be true that

E – W ≥ V

so that the clerk has enough to pay the toll.  If the clerk barely makes it, this inequality is an equality and

E – W = V.

The V at which this happens (for a given E and W) is called the cutoff toll Vo;  if Voltar were to increase the toll by any amount at all, the clerks wouldn’t get to cross the bridge.

It’s interesting to graph the cutoff toll Vo vs. money that customers have upon entering the store E.  You get something like this:

Photoelectric

Notice that the cutoff value of E is $1.00, which is the price of a bag of chips.  At or below this value the troll need not charge any toll at all, since no clerk will have any money to pay him.  That is, when V = Vo = 0,  then E = W.

WHAT’S GOING ON?

The physicists reading this blog have already guessed the game I’m playing: I have presented an analogy for Einstein’s explanation of the photoelectric effect (hence Toelek, from fotoelektrisch).  Make the following transformations:

Customers = photons;

Color of customer = frequency of photon;

Money = energy;

Store = photoelectric material;

Price of chips = work function;

Clerks = electrons;

Clerk’s money = kinetic energy;

Bridge = potential difference;

Voltar’s toll = kinetic energy required to jump the gap.

With these transformations, you can re-write the story as follows:

There is a photoelectric material, a metal such as platinum.  Inside the metal are electrons.  The electrons can be liberated if enough energy is added.

Now, the thing is, if you give energy to electrons to liberate them, the electrons don’t give any energy back: they’re greedy.  What’s more, they leave the metal immediately with whatever energy they have left over from the transaction.  However, the electrons don’t always get very far, because out behind the metal is a potential difference that the electrons have to cross in order for current to be observed.  Jumping this gap requires a certain amount of kinetic energy, without which the electrons don’t produce current.

How do we add energy to the metal?  Well, by shining light on it.  Light energy is quantized, in chunks called photons.  The energy of a single photon is proportional to its frequency, by Einstein’s formula E = hf.

Look, over there—I see some red light (E = 1.9 eV) approaching the metal.  Unfortunately, no electrons exit out the back, and consequently there is no current.  More and more red photons hit the metal, and a faster and faster rate, but it doesn’t matter.  There are no electrons coming out.

I conclude that the amount of energy need to liberate an electron (called the work function) is greater than 1.9 eV.

Later, I see orange light (E = 2.1 eV) go into the metal.  I now observe some electrons coming out, but none of these produce current.  I conclude that the work function is W = 2.1 eV.

Even later, I see yellow light (E = 2.18 eV) go in.  Electrons are coming out, and these can cross the potential difference.  The potential difference must be 0.08 volts or less.

There are many quantities which are important in analyzing this situation: the amount of energy a photon has before entering the metal (E), the work function (W), the voltage that electrons have to jump (V), and the amount of energy an electron has upon exiting the metal, K.  It should be obvious that

K = hf – W,

since the amount of energy an electron has upon exiting the metal is just the amount of energy a photon has upon entering the metal minus the cost of liberating an electron.  Additionally, for an electron (with charge e) to jump the gap, it must be true that

hf – W ≥ eV

so that an electron has enough kinetic energy to overcome the potential difference.  If the electron barely makes it, this inequality is an equality and

hf – W = eV.

The V at which this happens (for a given f and W) is called the stopping potential Vo.

It’s interesting to graph stopping potential Vo vs. energy of incoming photons E.  You get something like this:

Photoelectric2

Notice that the cutoff value of E is 2.1 eV, which is W.  At or below this value there need not be any potential difference at all, since no electron will be liberated.  That is, when V = Vo = 0,  then E = hf= W.

I hope you find this analogy useful.  As for me, I need to go to the store: all this talk of potato chips has made me hungry.

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Number form synesthesia or: why is there a kink at 20?

March 28, 2013 by Matthew Rave

Whenever I think of numbers, I form a mental image in my head.  This is not a conscious process; it happens consistently and involuntarily.  For example, whenever I imagine the numbers 1 through 100, I see something like this:

Numbers

You will note several interesting features of this mental map.  Firstly, there is always a 90° left turn at the number 20; there is always a 90° right turn at the number 100.  These two kinks are the only kinks in my mental number line; the lines are perfectly straight before zero and after 100.  Why the kinks are there is mysterious.

Notice also that the image is not to scale.  That is, 50 occurs half-way between 20 and 100 (why isn’t 60 there instead?)

Here’s another mental map I have, one that appears whenever I imagine a person’s age:

Age

You will note that this mental image is similar to the previous one, but rotated 90° to the right.  The scale is also warped: not only in the location of 50 yrs., but in the location of 10 yrs.  I believe this stems from my childhood belief that the years from age 10 to age 20 would seem to last longer than the years from 0 to 10.

Why childhood?  Well, I’ve had such mental images for as long as I can remember; it follows that they were first “constructed” in my brain at an early age.  And there is a sort of logic to the idea that 10-20 lasts “longer” than 0-10.  After all, we don’t normally recall anything about our first 5 years or so; to a child, it’s almost as if you missed those years.  So if I am 10 years old, say, and looking back at my life so far, it won’t seem nearly as long as the decade looming in front of me.  (I must stress that I am not a neuroscientist and that this is all pure speculation.)  As for why 50 is half-way between 20 and 100, I can only conclude that I wasn’t so good at calculating averages when I was younger.  The similarity of the two mental maps is best explained by positing that one of the maps is derived from the other, although which came first I cannot say.

But still, that kink…

I only became aware very, very recently that there is a name for this phenomenon.  These maps I make are called “number forms” and they are a form of synesthesia.  I have a friend who experiences grapheme-color synesthesia, seeing letters and numbers as if they had very specific colors.  It never occurred to me that my mental number maps were a related phenomenon in any way.

Here’s how I see the months of the year:

Calender

The order is always counterclockwise.  Strangely, the months are not quite evenly distributed: July is always at the top, but December/January are level at the bottom, with the (strange) consequence that there is one more month in the first “half” of the year than the second.  I also mentally divide the year into three partitions, starting at Sept. 1, Jan. 1, and June 1.  I am confident that this partitioning is a product of having attended school (on a semester system) for 25 years of my life.

Here’s the strangest map of all, but one that has (I think) the easiest explanation:

Years

This is how I picture the recent history of the world, from the late 1700’s to the present.  There are four kinks: at 1800, 1900, 1950, and 2000.  The three biggest wars (to an American, at least) are marked in red; 1968 is also clearly “labeled” in my mental map (obviously because it’s the year of my birth).  Again, there is a lack of scale: 1800-1900 takes up as much “space” as 1900-1950.  One might conclude that I regard the 20th century as more “important” than the 19th, since I relegate more space to the former.  But there is a simpler explanation.

I can still vividly recall a timeline of history that I saw, perhaps in the 3rd or 4th grade, that has the exact same topology as this last mental map of mine.  The years from 1800 to 1970 (or so) were graphically depicted in a timeline; there were folds at 1900 and 1950, simply to make the timeline fit on the printed page.  Above key years (such as 1939) were cartoonish drawings of world events, such as World War II or Man Lands on the Moon.  Beyond the 1970’s there was nothing.  I wish I could find this image, which I believe in some sense “triggered” this form of synesthesia; I want to say that the image was in a World Book Encyclopedia but I have no proof of this claim.

In any case, I think other forms of synesthesia may also be linked to the way we first learn certain things.  My friend (who sees colors for every letter of the alphabet) once told me the probable origin of his synesthesia.  He first learned letters and numbers through colored refrigerator magnets; the colors and letters became inextricably tied in his mind, and the connections exist to this day.  For any real neuroscientists out there, I believe this is a fruitful area for further research.

Anyway, I’d be curious to see how many other people experience “number forms”.  It doesn’t make you crazy.  After all, Sir Francis Galton called his book on the subject The Visions of Sane Persons.

But still, that kink…

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Can pessimism be comforting?

March 13, 2013 by Matthew Rave

flight

I don’t like to fly.

I will do it; I have flown dozens of times before; I will do it again.  But I don’t particularly enjoy the experience.  It has nothing to do with the perceived risk of flying…I know, of course, that driving on the highway is much, much more dangerous than getting into an airplane.  No, I don’t like to fly because it seems to me a particularly stressful way to die.  Seeing the wing shear off, then having the plane spiral down, gradually…

I don’t really want to talk about flying today.  What I want to talk about is a paradox that I discovered recently.  The paradox is this: the knowledge that magic is non-existent, that the universe is indifferent, that you are not special in the grand scheme of things—that knowledge can be both a comfort and a source of fear, simultaneously.  And that’s weird to me.  Shouldn’t one’s beliefs comfort you, or not comfort you, as the case may be?

Let’s say that you do think that you’re special, that you were meant for some grand purpose.  This would certainly be a comfort if you were afraid of flying.  After all, you’d say to yourself “why should I be afraid to get into an airplane?  It won’t crash—I’m special somehow!”

Now, suppose you are superstitious, and think you are special in the opposite way: you think you’re cursed, that the world is out to get you, that God hates you, whatever.  I bet that your beliefs don’t make flying a fun experience.

But what about me?  I am a physicist, a determinist, an agnostic, a free thinker.  You know how some people describe themselves as spiritual?  Whatever the opposite of spiritual is, I am that.  There’s no guardian angel watching over my shoulder; I was not meant for some higher destiny, and the universe doesn’t care about me one way or the other.  Given such beliefs, should I be comforted when I get on a plane, or not comforted?  Therein lies the paradox.

When I get on a plane, I often start thinking, “the wing’s going to rip off in mid-flight, I just know it…that would just be my luck…you just know I’m going to be on that one-in-a-million flight that crashes into the Grand Canyon.”  But then I comfort myself by saying “there’s no such thing as ‘being unlucky’.  I am no more likely than anyone else to be on an ill-fated Grand Canyon flight.  So I should take comfort, because objectively, plane crashes are really rather rare.”

The problem is, my beliefs also make me more nervous at times.  “There is no guardian angel.  I am not remarkable in any way, so I can’t be comforted by the idea that I am somehow special.  Planes sometimes crash, and there’s certainly a chance that I will be on such a flight.”

So: should I be comforted, or not comforted?

I should be comforted if I think (in some deep recess of my brain) that there really is something called bad luck, and that I really am “cursed” in some way, because when I remember that this is nonsense, I will feel better…my belief has erased a sense of foreboding that I was irrationally experiencing.

I should not be comforted if I think (in some deep recess of my brain) that there really is something called destiny, and that I really am “blessed” in some way, and that I was meant for some higher purpose than disintegration in a smoldering pile of twisted metal, because when I remember that this is nonsense, I will feel worse…my belief has erased a sense of protection and comfort that I was irrationally experiencing.

So again: should I be comforted, or not comforted?

Well, which is greater?  (1) My irrational belief (that everyone has to some degree) that I am cursed in some way, and that there is a “doom” hanging over me… or (2) my irrational belief (that everyone has to some degree) that I am blessed in some way, and that I was meant for something more?  In the first case (the pessimistic case) I should be comforted when I come to my senses, and in the second case (the optimistic case) I should be more worried when I come to my senses.

Hence the paradox:

  1. Pessimists are comforted when they remember that the universe is indifferent;
  2. Optimists are more worried when they remember that the universe is indifferent.

On balance, I am an optimist, which means my deterministic world view gives me even less comfort than it should.

Of course, given the fact that I am an optimist, I am comforted by the fact that there’s probably something wrong with my analysis.  Only, wouldn’t that make me a pessimist?  I’m so confused…

[Image is from the movie Flight (2012), directed by Robert Zemeckis.  It’s a good movie.  You should watch it.]

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What is your Google number?

March 6, 2013 by Matthew Rave

Kevin_Bacon

He should play Erdős in a movie…

My current Erdős number is 6.  I have collaborated recently with a mathematician (Jeff Lawson) whose number is 4; thus I fully expect to be “promoted” to an Erdős number of 5 within a year.

(What’s an Erdős number?  Basically, it’s the mathematical equivalent of the “Bacon number”.  You can read about Erdős numbers here.)

But I want to blog today about a different number that (frankly) I invented yesterday.  I call it a “Google number” (GN).  Here are the rules: what is the minimum number of words, none of which are proper nouns, that you must type into Google and do a Google search, such that the first search result is about you or one of your discoveries, written by you, or is a website written/maintained by you primarily?

I am very proud to say that my Google number is 2 (more on this later).

A Google number of 1 is very, very rare.  Type “president” into Google and you get a link to President of the United States…so Obama has a Google number of 1, but this will definitely change in 2017.  Type in “basketball” and you do not get Michael Jordan.  Type in “chess” and you do not get Carlsen, Kasparov, or even Fischer.

Einstein has a Google number of 1: “relativity” gives you an article on relativity.  James Cameron also has GN=1: “avatar” sends you to a James Cameron website, although you could argue that “avatar” is too close to the proper noun “Avatar” (there’s a lot of subjectivity here).    I’d be inclined to give a 1 to Thomas Edison since “incandescent” goes to an article on the incandescent bulb.  It’s not that easy to come up with more examples.  Try it yourself.

If you think about it, even the most educated person can’t have a vocabulary of much more than 30,000 words.  So logically, there can’t really be more than 30,000 or so people in the entire world with a Google number of 1.  This is 0.0004%, or 1 in 233,333.  Pretty select company.  And of course the actual number of people with Google number 1 is much, much lower, because a lot of words are “wasted”:  try searching for “harpsichord”, for example.  The lead search result does not point to any one individual person that I can see.  (Note: for simplicity, I define “Google number” as being English-specific; if we were talking about words in Spanish we might instead define a número Google, and so forth.)

What about a Google number of 2?  In theory there could be 30,000^2 = 900,000,000 people with a 2, but in practice this is fantasy.  Remember, you can’t use proper nouns.  Getting a 2 is very tricky.  Let’s try it with a famous person, to see how hard it is.  Let’s try Stephen Hawking.  “Black hole” doesn’t work; nor does “famous physicist” or “famous astrophysicist”.  “Hawking radiation” is off the table (see: proper noun.)  Even “grand design” doesn’t work because you get a British TV show first.  “History time” is a near-miss.  Finally, success: “brief history” works.  A Brief History of Time.  Hawking has a Google number of 2.

I would contend that anyone with some internet presence will have a finite Google number.  For example, my colleague Jeff (with the Erdős number of 4) has a Google number of 3: just type in “heuristic geometric phase” and you will get a talk he gave in Toronto on our joint research.  For all I know he may have a lower Google number, but it wasn’t that hard to get 3.

Now for some shameless self-promotion: my Google number is 2.  Type in “metaphor loop”.  I’m quite proud of this for some irrational reason.

One problem with this game is that it is fluid, ever-changing.  Douglas Hofstadter could very well write a book in which “metaphor loops” were integral; soon I would find my modest paper pushed to the side.  But that will happen to Obama, too, eventually, so I’m in good company.  C’est la vie.  For now, I’ll enjoy the fact that GN(me)=2, and I’ll await the vagaries of fate.

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Winston and Violet

March 5, 2013 by Matthew Rave

Winston Churchill and Violet Bonham Carter now appearing in: Many Worlds Comix #4!

churchill1

churchill2

churchill3

churchill4

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The Franck-Hertz ice cream truck

February 26, 2013 by Matthew Rave

Imagine that there’s an ice cream truck parked near a school.  It’s 3pm; class is dismissed and a steady stream of kids approach the truck.  For simplicity, let’s stipulate the following rules:

1. If a kid has enough money, he or she will buy an ice cream cone;

2. A kid will only buy one ice cream cone;

3. A kid will buy the most expensive ice cream cone he or she can.

After the kids buy ice cream (or not) they continue on their way, having whatever leftover money they might have in their pocket.

My question is this: by seeing how much money kids have left, what can you determine about the prices of ice cream cones?  (Astute observers will note that this toy model has many similarities to the Franck-Hertz experiment of 1914, but we’re not there yet.)

Let’s look first at some hypothetical data.  Here we have plotted L (money left over in a kid’s pocket) as a function of M (how much money a kid started with) for a school with 11 kids:

Franck 1

There doesn’t seem to be a pattern.  Maybe we don’t have enough data?  Let’s increase the number of kids to 42:

Franck 2

The sawtooth form of the function is characteristic of problems of this type, and can be understood intuitively.  First of all, notice that the function is linear to begin with, with a slope of exactly one; this means that below a certain threshold value of M, a kid can’t afford any ice cream, so he/she ends up with the same amount of money he/she started with.  Eventually, if M ≥ $1, a kid can buy a cone; L then plummets because the kid has spent a dollar.

It seems obvious from the graph, then, that ice cream cones are priced at $1, $2, and $3; beyond that we don’t have any data so can’t draw more conclusions.

Now, if we relax the stipulation that kids only buy one cone, then our data is ambiguous.  Maybe the cones are priced $1/$2/$3, or maybe cones are always just $1, and kids are buying more than one cone if they can.  We can’t distinguish between these cases; that’s why I put the original stipulation there to begin with.

Let’s try a more challenging graph:

Franck 3

This graph is much harder to interpret.  The first peak is much bigger than the others; there is also a very tiny peak on the right-hand side.  It helps if you know where the jumps are: L jumps down to zero whenever M is equal to $0.67, $1.02, $1.34, $1.69, $2.01, and $2.04.  If you want to work out the ice cream cone prices for yourself, feel free.  I’ll wait.

The solution?  A little trial and error will give you two different prices for ice cream cones: A= $0.67 and B=$1.02.  Then the jumps occur at A, B, 2A, A+B, 3A, and 2B.  If we were doing physics, we’d make a prediction: we would expect the next jump to occur at $2.36, which is B+2A.  Observing this would support our hypothesis.  But if the next jump occurred at $2.22, say, then we’d have to revise our theory and posit a new ice cream C priced at $2.22.

What does any of this have to do with physics?

I use this example when I introduce the Franck-Hertz experiment to my students.  This experiment was first performed in 1914 (an auspicious year!) and provided support for Bohr’s idea that atoms have specific (quantized) energy levels.  Electrons are accelerated and shot towards mercury atoms (in a vapor).  The electrons may then give energy to the atoms (exciting them) or they may not, bouncing off without loss of kinetic energy.  We look at how much energy the electrons have to start with, and how much they end up with, and thereby deduce the energy levels of the mercury atoms.

How is that possible?  In terms of the analogy, make the following transformations:

kids –> electrons

ice cream truck –> Hg atoms

kids buying ice cream at certain prices –> electrons giving certain amount of energy to Hg atoms

prices of ice cream cones –> energy levels of Hg

M (initial amount of money) –> V (proportional to initial kinetic energy of electron)

L (leftover money) –> I (proportional to final kinetic energy of electron)

If energy levels of an atom are truly quantized, then we would expect a graph of I vs. V to look like our graphs above, with an increasing sawtooth pattern.  Where the drops occur will then tell us the specific energy levels of the Hg atom.  (Incidentally, why do we use V and I?  Well, in the actual experiment the easiest way to measure initial kinetic energy is by measuring the voltage used to accelerate the electrons; the easiest way to measure final kinetic energy is to measure the current of the electrons after they have passed through the Hg vapor.)

How did the experiment go?  Here are the results:

525px-Franck-Hertz_en.svg

It should be obvious that atomic energy levels have specific “prices”, and that there’s a minimum amount of energy that an electron must have in order to “buy” an atomic transition (exciting the atom at the expense of the electron’s kinetic energy).  It remains for the experimenter to do some elementary unit conversions, to translate I and V into final and initial kinetic energy.

[Note for advanced students and/or physicists: it is interesting to ponder the following questions, which highlight the fact that the ice cream analogy is not perfect: (1) why is the I vs.V graph not linear at low voltage? (2) After “spending” kinetic energy to cause the first excited state, why does the electron’s energy not drop all the way down to zero?]

Posted in Physics | Tagged , , | 6 Comments »

Asteroid/meteor as a 1 in 100,000,000 coincidence? Not really…

February 23, 2013 by Matthew Rave

asteroid

CNN recently posted a story about how the Feb. 15 asteroid/meteor event was very, very unlikely: a 1 in 100,000,000 coincidence.  I disagreed.  I was all ready to blog about how CNN, yet again, got a non-scientist to write about science…and my indignation was already half out of the bottle.

Then I saw who wrote the article: Meg Urry, a highly respected Yale astrophysicist.

So, I sat on my hands for a second and re-evaluated the article.  It does not contain any errors as far as I can tell.  But I still contend that the article is misleading: saying that the asteroid/meteor event was a 1 in 100,000,000 coincidence is the wrong way to look at it.

I agree that if you multiply 1 in 3,650 days times 1 in 36,500 days you get something close to 1 in 100,000,000.  But all you’ve proven is that for any given random day, there is only a 1 in 100,000,000 chance of such a coincidence occurring.

However, we now live in a post-Nate Silver, post Bayesian controversy world, right?  We’ve known about asteroid DA14 for exactly a year (as of today).  So the right question to ask, before it flew by last week, was: what is the chance that a human-injuring meteor will fly by on the same day?  Well, given that an asteroid will already pass that day, the chance of a once-in-a-decade meteor flying by that same day is just 1 in 3,650 (that is, once in a decade).

I have the utmost respect for Dr. Urry.  I suspect that the hyperbole-filled title of her CNN post was written by a CNN webmaster, not her.  I still agree that the coincidence was unlikely, but given that DA14 was already expected to fly by, the Chelyabinsk meteor hitting on the same day does not sink into the realm of unbelievability.

[Trivia note: Chelyabinsk is the birthplace of Evgeny Sveshnikov, the chess grandmaster for whom the Sveshnikov variation of the Sicilian defense is named.  And I do know that, as much as I like the Sveshnikov defense, I tend to go down in flames like a meteor whenever I play it.]

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The top 10 foods I would not have eaten as a kid

February 19, 2013 by Matthew Rave

The following is a list of foods I love today, at the age of 44.  I can’t imagine the 10-year-old me even trying any of these foods, much less liking them.  But we grow up; our tastes change, and hardly a day goes by without me craving Marmite.  I mean, come on?  Isn’t that weird?  Please tell me I’m not crazy!

10. Fresh spinach

WU0210H_perfect-spinach-salad

I didn’t really learn to enjoy salads all that much until I discovered that fresh spinach is infinitely tastier than lettuce.  As a kid, I think I tried spinach, in a can, like Popeye; the problem is, canned spinach is barely edible.  When you eat a fresh spinach salad, maybe with apples and a splash of bacon vinaigrette, you can only wonder: is this really the same plant as found in canned spinach?  Hard to believe.

 

 

9. Snails

Escargot

I’ll be honest; I’ve only had snails (at most) 10 times in my life, and always in a fancy restaurant.  But they’re tasty.  They taste even better when you call them snails, since calling them escargot leaves a bit of a snooty aftertaste.

 

 

8.Soft-shelled crab

crab

 

I first tried this in a Thai curry dish.  I still find the texture a bit strange, but overall I find the taste delectable.

 

7. Mushrooms

mushrooms

 

I’ve liked mushrooms for a long time, but can’t recall whether I tried them as a kid or not.  I think most Americans are first exposed to mushrooms as a topping on pizza, but I don’t really like mushrooms that way.  They invariably go straight from a can to the pizza.  Fresh mushrooms are better, and stuffed mushrooms may be the best of all.  As a bonus, there are many, many varieties, and they all taste different.

 

6. Mortadella

mortadella_620x465

To my mind, mortadella is the king of sandwich meats.  It’s a bit like deli bologna, but more flavorful: it is marbled with pork fat, and often has pistachios and olives mixed in.  I might have liked this as a kid, but I never tried it.  I had never even heard of it.  I’d have to drive over a hour from where I live to find this today.

 

5. Runny eggs

eggs

Yolk freaks kids out.  But not me.  Over-easy is the way to go.  And when the Hollandaise in an Eggs Benedict runs together with the yolks…

 

4. Coffee

coffee

I guess I haven’t grown up entirely.  I don’t drink coffee, unless it’s cold with plenty of milk and sugar.  Sort of like a melted coffee ice cream.  My favorite way to have coffee is the way they serve it in the Vietnamese restaurants: over ice, with sweetened condensed milk.

 

 

3. Pomegranate juice

POM

So bitter.  Yet so good somehow.  I don’t really know why I like it.

 

2. Stilton

stilton1

The king of cheeses.  Radically strong flavor; almost hallucinogenic.  Not just for Wallace and Gromit anymore.

 

1. Marmite

marmite

What can I say?  Marmite, objectively, doesn’t taste all that great: it’s almost pure umami, like chewing on a bouillon cube.  And yet it is alluring for some unfathomable reason.  On bread, with butter, it is divine; mixed with honey and corn syrup, it is the ideal pizza sauce.  I can get Marmite (or its complex conjugate, Vegemite) where I live, but I don’t eat it all that often.  I may go 6 months without having any.  Then, on a random day…the 19th of February, say…I will start to crave it, and even start to blog about it.

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What color is the bear? A new class of solutions

February 17, 2013 by Matthew Rave

In the 1985 film Young Sherlock Holmes, Holmes tells Watson the following riddle:  “You’re sitting in a room with an all-southern view.  Suddenly, a bear walks by the window. What colour is the bear?”  (He says “colour” not “color” because he’s from the UK.)  As I recall it takes Watson most of the movie to give the obvious answer—white—because the bear must be a polar bear.  All southern view…North Pole…polar bear…you get the idea.

young-sherlock-holmes-watson-sherlock

Over the years I’ve hear other versions of this riddle.  The most common seems to go something like this: “A hunter travels a mile south, a mile east, shoots a bear, then travels a mile north to her starting point.  What color was the bear?”  People assume that this riddle is isomorphic to the previous one, because (supposedly) there is only one place on Earth you can travel the same distance south, then east, then north, and return to the beginning.  But this is wrong.  There are an infinite number of places on Earth you can travel in a loop that is 1 mile south, then 1 mile east, then 1 mile north.

Of course, starting at the North Pole is one solution.  But there are also many, many more solutions close to the South Pole.  Imagine, for example, a latitude roughly 1/(2π) miles north of the South Pole; in such a case the parallel along that latitude is the circumference of a circle, given by

C = 2πr = 2π [1/(2π)] = 1 mile.

(I said roughly because we’re on the surface of a sphere, so the circumference of a parallel is not exactly 2πr—because r is an arc length, not a straight line—but 1 mile is so much smaller than the radius of the Earth that we can assume a locally flat geometry.)  If a hunter started his journey 1 mile north of this latitude, then of course he could go 1 mile south, then 1 mile east (circumnavigating the South Pole!) and then 1 mile north, and return to his starting point; I presume there would be no bears.

South Pole

There are actually infinitely many solutions that work.  In each case, after going a mile south, the hunter would have to reach a latitude in which the circumference C was an integer fraction of 1 mile.  That is, it must be true that

C = 1/n miles,

where n is an integer.  This means that the parallel would have to be

r = C/(2π) = 1/(2πn)

miles from the South Pole (again, this is a flat approximation to a spherical problem).  So the most general South Pole solution is that the hunter should begin 1 + 1/(2πn) miles north of the South Pole.  For example, take n = 5.  If a hunter starts 1.0318 miles from the South Pole, she can go south 1 mile, east 1 mile (circumnavigating the South Pole exactly 5 times) then north 1 mile, and relax in her hot tub.  No bears will be harmed, unless some evil genius has released them in Antarctica.

The original version of the riddle, as given by the young Sherlock Holmes, is superior, since it has only one solution.  We can conclude that Sherlock Holmes was good at math.

I mean, maths.

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The phantom crane fly

February 4, 2013 by Matthew Rave

One day in the summer of 2011, while mowing the lawn, I saw a strange creature flying through the air.

Actually, “flying” is too generous a term.  The creature was lilting through the air.  Lurching.  It appeared to have ten legs, and was about the size of a silver dollar.  I was puzzled, to say the least, but that lawn wasn’t going to mow itself so I went back to work.

dip_phantom_crane_fly01

The mystery bug…

I live in a rural area in the mountains of North Carolina, only 30 minutes away from the entrance to the Great Smoky Mountains National Park.  There’s a lot of wildlife here: I’ve seen bear, elk, deer, raccoons, opossums, groundhogs, voles, and squirrels; our bird feeders are always full of cardinals, chickadees, towhees, finches, and titmice; and I once came home to a 4-foot black snake inside my house.  As for arthropods, I’m very familiar with flies, no-see-ums (family Ceratopogonidae), moths, wasps, honeybees, crickets, ants, beetles, and spiders of all kinds.  I’ve had close encounters with black widow spiders no less than 3 times in my life.

But this thing?  With 10 legs?  Lurching through the air like a drunken hang glider?  Incomprehensible.

Over the course of that summer, I saw such creatures on numerous occasions.  I gradually came to realize that they were insects, since subsequent sightings showed 6 legs, not 10.  My working hypothesis was that what I saw that first day was a mating pair: two of these things stuck together.  But I still had no idea what the confounded creatures were.

In appearance, the insects were bizarre to say the least.  They were striped, like zebras, and their legs appeared  to have at least 3 joints each, so that the legs took on a zigzag character.  They didn’t appear to use their wings, which I guessed were vestigial; rather, picture a 6-legged starfish up on one end, clawing and grasping its way forward.  As a physicist, it looked very much like the creatures were literally swimming through the air.  And so I resolved, with the help of the internet, to positively identify them.

Rutherford said that “all science is either physics or stamp collecting.”  A lot of people take this to be a disparaging comment about sciences other than physics, but I don’t.  I kind of like stamp collecting.  I like being meticulous, and being detailed.  That’s why I like pastimes such as putting together 1000-piece puzzles.

But my search for the identity of the “mystery bug” took stamp collecting to a whole new level.  It literally took me a month of sleuthing to identify the things.  I tried the obvious first: I googled things like “strange zebra striped bug” and “bug that swims in the air” but had no luck.  I posted a question on an entomology bulletin board.  I looked at websites dedicated to “insects of the Appalachians.”

Finally, I had a breakthrough: I saw one of the bugs hitting up against a window in our house.  For the first time, I could see the creature close up and for more than just a second or two.  I verified that the creature did have six legs; I verified that it did have wings, although they seemed useless.  I realized that my mystery bug was a crane fly.  Here’s a more typical, run-of-the-mill crane fly:

800px-Crane_fly_halteres

A typical crane fly

Regular crane flies are common where I live; kids often mistake them for gigantic mosquitoes (which they are not).

Once I realized that the mystery bug was a type of crane fly, my task was eased enormously.  And eventually I found this assortment of photographs.  Eureka!  I had done it!  They were phantom crane flies, of the family Ptychopteridae.  Specifically, they were the species Bittacomorpha clavipes, which, according to this Wikipedia article, are “known for the odd habit of spreading out [their] legs while flying, using expanded, trachea-rich tarsi to waft along on air currents.”

It turns out that the phantom crane fly is one of the very, very few creatures on Earth that fly without using their wings.  They are literally swimming, somehow taking advantage of a high Reynolds number (let’s say, 265?) to sludge through the atmosphere without those wings that evolution gave them.  Consequently they look more like seed pods drifting on the wind than they do insects.

What is my point?  I don’t have one.  I just think these bugs are cool, and you should try to find them if you ever visit the Eastern United States.  They hang out in marshy areas in late summer.  Oh, and if you’re a physicist or an entomologist, think about studying these little guys.  The field’s wide open as far as I can tell.  Somebody needs to video the flight of the phantom crane fly, so get on it!  [Note added later: I did find this video which shows the weird flight, are there more?]

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